The number 8064
8064 is a composite number with 48 divisors. Its prime factorisation is × × 7. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32 … 8064.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8064: a Harshad number: divisible by its digit sum 18.
- 2
8064 is composite. Its prime factorisation is
- 3
The divisors add up to 26520; without 8064 itself that is 18456, so 8064 is abundant (18456 is more than 8064). Euler's totient φ(8064) = 2304 numbers up to 8064 share no factor with it.
- 4
The digits of 8064 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 114 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8064 = 2^{7} \times 3^{2} \times 7 \]8064 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 26520 |
| Euler totient φ(n) | 2304 |
| Square | 65028096 |
| Cube | 524386566144 |
| Square root | 89.799777 (= 24√14) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 114 |
| Scientific notation | 8.064 × |
8064 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and sixty-four |
| Binary (base 2) | 1111110000000 |
| Octal (base 8) | 17600 |
| Hexadecimal (base 16) | 1F80 |
| Base 3 | 102001200 |
| As time | 8064 seconds = 2 h 14 min 24 s |
Is 8064 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8064 ÷ 2 = 4032) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8064 ÷ 3 = 2688) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8064 ÷ 4 = 2016) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8064 ÷ 6 = 1344) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (8064 ÷ 7 = 1152) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (8064 ÷ 8 = 1008) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (8064 ÷ 9 = 896) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8064 ÷ 12 = 672) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8064 a prime number?
No. 8064 = × × 7, so it is divisible by 2.
What are the factors of 8064?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 288, 336, 384, 448, 504, 576, 672, 896, 1008, 1152, 1344, 2016, 2688, 4032, 8064.
What is 8064 in binary?
1111110000000 (hexadecimal 1F80, octal 17600).
What is the square root of 8064?
About 89.7998, exactly 24√14.
Is 8064 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 8064?
8064 is a Harshad number: divisible by its digit sum 18.